document.write( "Question 90323This question is from textbook Algebra and Trigonometry
\n" ); document.write( ": Give the center of the circle with equation x squared+2x+y squared+22=0 \n" ); document.write( "

Algebra.Com's Answer #65558 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
You would like to get your equation into the standard form for a circle:
\n" ); document.write( " $\"%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2\"$ where the center is at (h, k) and the radius is r.
\n" ); document.write( "Starting with:
\n" ); document.write( " $\"x%5E2%2B2x%2By%5E2%2B22+=+0\"$ First, complete the square in the x-terms by adding the square of half the x-coefficient ( $\"%282%2F2%29%5E2+=+1\"$ ) to both sides.
\n" ); document.write( " $\"%28x%5E2%2B2x%2B1%29%2B%28y%5E2%29%2B22+=+1\"$ Now subtract 22 from both sides.
\n" ); document.write( " $\"%28x%5E2%2B2x%2B1%29%2B%28y%5E2%29+=+-21\"$ Factor the trinomial in x.
\n" ); document.write( " $\"%28x%2B1%29%5E2%2B%28y%2B0%29%5E2+=+-21\"$ Now compare with the standard form for a circle:
\n" ); document.write( " $\"%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2\"$ ...and you can see that h = -1 and k = 0
\n" ); document.write( "So the center is at: (-1, 0)
\n" ); document.write( "Notice that the radius,( $\"sqrt%28-21%29\"$ ) is an imaginary number! \n" ); document.write( "

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